Abstract. In this letter, we consider a quasi–two-dimensional (Q2D) system of widely separated spheres suspended in a quiescent fluid and in contact with a planar fluid-gas interface. We construct and estimate the accuracy of two generic approximations to the translational-translational mobility, needed, e.g., in Brownian simulations. Both simplifications for Q2D systems are shown to be essentially different than their three-dimensional well-known analogs. First, we discuss the asymptotic form of the Q2D two-sphere mobility up to cubic order in the inverse inter-particle distance and compare it with the corresponding three-dimensional Rotne-Prager expression. We also explain how to avoid divergences due to lubrication forces at the contact. Next, we construct the Q2D mobility of point-particles, which—unlike in 3D—is not pairwise additive. Finally, we determine the range of validity of both long-distance approximations by computing numerically exact results.

PACS numbers: 47.15.Gf, 82.70.-y

Print publication: Issue 3 (August 2004)
Received 13 April 2004, in final form and accepted for publication 24 May 2004